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Induction
Giambattista 20.46-47
Problem:
• A solenoid of length 2.8 cm and diameter 0.75
cm is wound with 160 turns/cm, and carries
current of 0.2 A. What is the flux through one
of the windings?
• The current is now decreasing at a rate of 35
A/s, what is the induced EMF in one winding?
• What is the induced EMF in the entire
solenoid?
2
Relevant ideas:
3
Relevant ideas:
• A solenoid is idealized as a certain number of
current loops of diameter d in series.
4
Relevant ideas:
• A solenoid is idealized as a certain number of
current loops of diameter d in series.
• The current loops create a magnetic field. This
field permeates each loop, ie, there is
magnetic flux through each loop.
5
Relevant ideas:
• A solenoid is idealized as a certain number of
current loops of diameter d in series.
• The current loops create a magnetic field. This
field permeates each loop, ie, there is
magnetic flux through each loop.
• EMF is generated when the flux changes. In
this way the solenoid counteracts rapid
changes: electromagnets display inertia.
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Equations associated with ideas:
7
Strategy
Strategy
• Determine the number of turns from the
length and given winding rate.
Strategy
• Determine the number of turns from the
length and given winding rate.
• Calculate the strength of the magnetic field
produced by the solenoid, then the flux
through one turn (winding).
Strategy
• Determine the number of turns from the
length and given winding rate.
• Calculate the strength of the magnetic field
produced by the solenoid, then the flux
through one turn (winding).
• Calculate the rate of change of the flux from
the rate of change for the current, deduce the
EMF for one turn. Sum EMF from N windings.
Solution
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